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There are many people who think that the Affordable Care Act (ACA) is bad policy. I am among them. There are also many who think that the current trajectory of government spending is unsustainable and economically harmful. I am also among them.

Then there are people who think it would be wise to shut down the federal government if they can’t get language passed that threatens to defund the ACA. (Notice that I didn’t say language that “defunds the ACA”; I said language that “threatens to defund the ACA.” Much of the ACA is actually funded through mandatory spending so Congress would need to pass a full repeal of the bill to defund it. What these folks want is language in the budget resolution saying that the ACA ought to be defunded. The bill might strip out some discretionary funding but most of the ACA would go forward.)

I am not among them.

To help us think through the options, let’s borrow from game theory and employ a decision tree. The House (H) can either choose to pass a continuing resolution (CR) that funds the ACA or a CR that calls for de-funding the ACA. The Senate (S) can choose to pass whatever the House sends them or to reject it. If they reject it, and no CR is passed by October 1, the federal government will shut down. In this case, as the CRS puts it, “substantial ACA implementation might continue during a lapse in annual appropriations that resulted in a temporary government shutdown.” If the Senate passes whatever the House sends them, then it will go to the President (P) who can either sign it or veto it.

At the end you can see the outcomes and the way that each group feels about them.

Options are happy, sad, neutral, and outwardly sad but secretly happy. (click on the images to enlarge):

To figure out the most likely outcome (the “equilibrium”) you do a fancy thing called “backwards induction.” It is actually quite simple: think about how each player would act at each stage, starting at the end of the game, and cross off implausible actions. This will help you eliminate unlikely outcomes. This is what I’ve done below, with dashed lines indicating an action that a particular player is unlikely to take.

We can with confidence cross off the possibility that the President will veto a CR that keeps the government open and fully funds his signature initiative or that the Senate would reject such a bill.

We can also cross off the possibility that the President would sign or that the Senate would send him something that calls for defunding his signature initiative.

That leaves us with two plausible scenarios: the House doesn’t use the CR as a means to attack the ACA, the CR passes the Senate, and the President signs it. This is the top branch of the game tree. House Republicans will be neutral about this outcome since they will have escaped blame for a shutdown but will have done nothing to stop the ACA. Senate Democrats and the White House will be pleased.

The other somewhat plausible scenario is that the House passes a CR calling to defund the ACA, and the Senate rejects it. The government would shut down and the ACA would mostly be untouched. I’m guessing Republicans would get most of the blame for shutting down the government since they lack a bully pulpit, aren’t as gifted as the president at communicating, and the ideological stereotype is that Republicans would like to see the government shut down any way. The White House and Senate Democrats will be outraged—simply outraged—that Republicans would do this but they will secretly be happy to have one more reason to say Republicans should never be trusted with power.

If Republicans see all of this, they will likely flinch, hold their noses, and pass a CR that doesn’t touch the ACA and hopefully come up with more constructive ways to challenge the policy. But, it is a close call for some House Republicans so for this reason, I’ve only partially crossed off the first bottom fork of the decision tree.

What the tree doesn’t indicate is the long run consequences of a government shutdown. Two and a half years ago, when Washington was staring down a different government shutdown, I drew from the experience of U.S. states to conclude that a shutdown is not in the interest of those who advocate for limited government:

As is often the case, we can look to the American states for some guidance. It turns out that in 23 U.S. states, the government will automatically shut down in the event that the governor and the legislature fail to agree on a budget. In his work on budget rules, David Primo examined the theoretical impact of these provisions from a game theoretic perspective. He noted that in states with an automatic shutdown provision, “the legislature will be able to achieve its ideal budget, so long as the governor prefers it to no spending.” (p. 102)

He therefore predicted that states with such a provision will spend more than states without such a rule. He then tested the hypothesis, controlling for a number of other factors known to impact state spending and found that states with an automatic shutdown provision actually spend about $64 more per capita than other states. As he notes, “This effect is remarkably large, given that shutdowns occur rarely.” (p. 103)

This suggests that the federal government’s automatic shutdown provision—by making Congress’s desired spending level a take-it-or-leave-it offer—tends to bias the government toward more spending. By extension, it also suggests that a government shutdown will shift negotiating power toward those who favor more spending. So, paradoxically, fiscally conservative tea partiers stand to lose the most if the federal government shuts down.